Question

How do you solve 3/(n-1) = 2n/(n+4)

Answer 1

Answer: n= 4 , (-3/2)

Explanation:

Your goal is to isolate n by getting it by itself

Multiply both sides by (n-1) to get 3 = ((2n)(n-1))/(n+4)

Use distributive property on the 2n * (n-1) to get 3 = (2n^2 - 2n)/(n+4)

Multiply both sides by (n+4) to get 3n + 12 = 2n^2 - 2n

Subtract 12 and 3n from both sides to get 2n^2 - 5n -12 = 0

Solve the quadratic using any method you like

Factoring would give you (n - 4)(2n + 3) = 0

So n= 4 and -3/2

Answer 2

Explanation:

To solve the equation 3/(n-1) = 2n/(n+4), follow these steps:

Step 1: Cross-multiply to eliminate the fractions.

3 * (n + 4) = 2n * (n - 1)

Step 2: Distribute the terms on both sides.

3n + 12 = 2n^2 - 2n

Step 3: Move all terms to one side and set the equation to zero.

2n^2 - 5n - 12 = 0

Step 4: Factor the quadratic equation, if possible. In this case, we can factor by finding two numbers that multiply to -24 and add to -5.

(2n + 3)(n - 4) = 0

Step 5: Use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

2n + 3 = 0 or n - 4 = 0

Step 6: Solve for 'n' in each equation.

2n + 3 = 0 => n = -3/2

n - 4 = 0 => n = 4

So, there are two possible solutions for 'n': -3/2 and 4.